Complex ridgelets for shift invariant characterization of surface topography with line singularities

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Abstract

A complex ridgelet transform, which provides shift invariance and good performance for line singularities, is proposed to solve the problems with existing wavelet-based methods in surface metrology by taking a dual-tree complex wavelet transform on the projections of the finite Radon transform. Numerical experiments show the efficiency of this methodology in approximation, denoising, and characterization of engineering and bioengineering surfaces with straight scratches.

Original languageEnglish
Pages (from-to)423-431
Number of pages9
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Volume344
Issue number6
Early online date5 Jul 2005
DOIs
Publication statusPublished - 19 Sep 2005

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Surface topography
topography
bioengineering
Radon
shift
Invariance
radon
wavelet analysis
Wavelet transforms
metrology
invariance
projection
engineering
methodology
approximation
Experiments
Bioengineering

Cite this

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title = "Complex ridgelets for shift invariant characterization of surface topography with line singularities",
abstract = "A complex ridgelet transform, which provides shift invariance and good performance for line singularities, is proposed to solve the problems with existing wavelet-based methods in surface metrology by taking a dual-tree complex wavelet transform on the projections of the finite Radon transform. Numerical experiments show the efficiency of this methodology in approximation, denoising, and characterization of engineering and bioengineering surfaces with straight scratches.",
keywords = "Line singularities, Radon transform, Ridgelets, Shift invariance, Surface characterization",
author = "Jianwei Ma and Xiangqian Jiang and Paul Scott",
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AU - Jiang, Xiangqian

AU - Scott, Paul

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N2 - A complex ridgelet transform, which provides shift invariance and good performance for line singularities, is proposed to solve the problems with existing wavelet-based methods in surface metrology by taking a dual-tree complex wavelet transform on the projections of the finite Radon transform. Numerical experiments show the efficiency of this methodology in approximation, denoising, and characterization of engineering and bioengineering surfaces with straight scratches.

AB - A complex ridgelet transform, which provides shift invariance and good performance for line singularities, is proposed to solve the problems with existing wavelet-based methods in surface metrology by taking a dual-tree complex wavelet transform on the projections of the finite Radon transform. Numerical experiments show the efficiency of this methodology in approximation, denoising, and characterization of engineering and bioengineering surfaces with straight scratches.

KW - Line singularities

KW - Radon transform

KW - Ridgelets

KW - Shift invariance

KW - Surface characterization

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